Improving AA in Cycles / Removing jaggies
Here's an example of a similar problem I'm facing at the moment.



Here the ribbed feature of the can happens to be on the boundary of pixels for every rib, this means cycles won't know which colour to make most important (that would require spatial antialiasing), it doesn't have contextual information that our brains have. This is the Moiré effect, it almost looks transparent.

But if I zoom in and render just the can at higher resolution it's obvious that the geometry is fine.



I may be wrong, but I think this is an edge case which directly relates the feature size being so close to pixels and that causes the jaggie pattern to emerge. As for extra AA, cycles does AA implicitly I think it's part of the algorithm, if it's getting it wrong there's little that can be done (without changing the geometry a little)

This may seem like a lazy answer, but it's normal to render at higher resolution than the final needed render, and sample down in post-processing to help the AA. In the case where you have features which are about the same size as a pixel (or in a pattern of every 2nd pixel), this becomes important. It's easier to sample down once you have all the right pixels than it is for Cycles to perform AA with insufficient information.

Other helpful ways to reduce jaggies are: 


bevels to make the surface edges less abrupt (help guide the light)


but make sure the bevels are finer grained than the pixels used to represent them, so go for a multi-cut fillet if you can spare the geometry.

add imperfections (most surfaces are not flawless..it all contributes to realism and helps break up unwanted patterns)
softer lighting, more bounces.
The post processing tab has a Dither option to help avoid banding, worth seeing if that tames the effect a bit.
reduce the glossyness, or specular effect, it will be most noticable at the corners. that means the difference between:

and